Talk:Playfair's axiom

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 Field: Geometry

Almost nonsense[edit]

Not only are sections of this article poorly written, but there is also a knotty problem with the section on the relationship to Euclid's 5th postulate. The article repeats the near-nonsense that can be found in Henderson's text - and that's the rub, this is sourced material. The argument goes – they are not equivalent since one holds in spherical geometry and the other doesn't. Leaving aside Henderson's deliberate confounding of spherical and elliptic geometry (there is a viewpoint from which this makes sense, but that is a very abstract advanced topic which does not belong at this level of treatment), the only thing that this argument shows is that the two concepts are not tautologically related. This is a straw-man argument, no one to my knowledge has ever claimed that the statements were logically equivalent. The equivalence must be established within the context of the geometry in which the statements make sense. Without that context (that is, the axioms which define the geometry) one can not provide a proof that either statement implies the other. What can be said in this situation is that the two statements are equivalent in the context of Euclidean geometry, while they are not equivalent when interpreted in the spherical model. Henderson's fixation on the spherical model distorts the way he emphasizes his statements and it is this distortion which is being repeated in this article. Conclusions about which statement is "stronger" just don't make any sense. It is not clear to me how I should fix this without just wiping it all away. Bill Cherowitzo (talk) 18:03, 9 October 2013 (UTC)

It appears that Henderson has come out with a new edition and has picked up a co-author. Circumstantial evidence indicates that the language has been toned down and is now in line with what I have written above (but I haven't seen a copy of this edition). I think I can now rewrite the offending section appropriately. Bill Cherowitzo (talk) 22:44, 9 October 2013 (UTC)